EP2283374A1 - Anordnung von spulen für eine mri-vorrichtung - Google Patents
Anordnung von spulen für eine mri-vorrichtungInfo
- Publication number
- EP2283374A1 EP2283374A1 EP09741593A EP09741593A EP2283374A1 EP 2283374 A1 EP2283374 A1 EP 2283374A1 EP 09741593 A EP09741593 A EP 09741593A EP 09741593 A EP09741593 A EP 09741593A EP 2283374 A1 EP2283374 A1 EP 2283374A1
- Authority
- EP
- European Patent Office
- Prior art keywords
- magnet
- region
- coil
- field
- current
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
- G01R33/381—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using electromagnets
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves
- A61B5/055—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
- G01R33/3806—Open magnet assemblies for improved access to the sample, e.g. C-type or U-type magnets
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
- G01R33/381—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using electromagnets
- G01R33/3815—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using electromagnets with superconducting coils, e.g. power supply therefor
Definitions
- the present invention relates to a magnet arrangement and a method of determining a magnet arrangement, and in particular, a magnet arrangement for use in MRI (magnetic resonance imaging) or other similar applications.
- MRI magnet system typically one desirable characteristic of an MRI magnet system is the ability to generate a strong and homogenous axial magnetic field over an imaging region, which is commonly referred to as the diameter sensitive volume (DSV). It is also desirable to restrict the peak magnetic field produced inside the superconductors themselves, and minimize the stray field external to the assembly.
- DSV diameter sensitive volume
- the minimization of stray fields is a process generally referred to as shielding, and is historically achieved by placing coils as part of the assembly on the exteriors of the field producing magnet, to essentially reduce the stray field of the magnet and to minimize the size of the fringe field.
- active shielding is a process whereby coils with reverse current directions are placed on top of the main winding to reduce stray magnetic fields exterior to the magnet chamber.
- Other factors that influence the design and manufacturing of magnets are related to geometrical constraints, that is, to reduce the magnet size, weight and associated wire cost, and the time taken to wind the individual coils that collectively comprise a magnet.
- US2005/0146332 describes a magnetic field generator for producing a homogenous magnetic field region and a method of designing an MRI system that produces a low fringe field region.
- the method comprises defining a solution space, defining a field of view, a centre field and homogeneity requirements, defining fringe field requirements, and running an optimization algorithm to determine coil positions.
- the optimisation algorithm does not yield a single global optimum solution, and consequently leads to localised minima, making the determination of an optimum layout complex.
- US-6,255,929 describes a method of making optimized electromagnets. Whilst the described technique allows the magnet design optimization problem to be cast as an Ll -norm minimization linear programming calculation, for which a global solution can always be found, limitations still exist.
- the magnets are optimized to require the least amount of dissipated power for the given predetermined axial magnetic field, which can only be used for resistive and not superconducting magnets.
- superconducting magnet designs are produced by minimising the length of superconducting wire used. Thus, different analysis is required for superconducting and resistive magnets.
- the minimisation process is based on a constant current density coil configuration, which does not necessarily result in an optimum magnet design. Furthermore, the global solution arises from casting the problem as a simpler Ll -norm minimisation calculation allowing a global solution within the constrains of the specified functions and does not therefore represent a optimum magnet configuration.
- the approach also employs a virtual coil comprising an infinitesimally thin conductor.
- Each iteration of the design process requires an update of the virtual coil, which makes the process inappropriate for superconducting coil design. This is highlighted by the fact that the method only caters for unshielded long magnets in which each of the coils are wound in the positive sense.
- US-5,760,582 describes gradient coil assemblies and shim coil assemblies for magnetic resonance imaging (“MRI") devices, wherein the coil assemblies comprise a coil support and a conductive wire having a locus described by a solution of a current continuity equation over a finite interval for which certain terms of the magnetic field expansion are equal to zero, to generate non-uniform magnetic fields.
- the gradient coil produces gradient magnetic fields and linear magnetic fields which cancel non-uniformities in the magnetic field of the magnet of the MRI device. Shim coils can be used to cancel such non-uniformities, as well.
- US-5, 382,904 describes superconducting electromagnets suitable for use in the NMR tomography of human organs.
- Each of the disclosed electromagnets are constructed according to a methodology for structured coils, where the desired field at locations within - A -
- the volume of interest and, optionally, outside of the location of the coils is selected; the current magnitude and polarity for a plurality of coil element locations are then optimized, by way of a computer program, to provide the desired field magnitude at the locations.
- the magnet construction results in a plurality of coils of varying current polarity, and of irregular shape and size, optimized to provide the uniform field within the DSV.
- the irregular coil shapes are difficult to produce in practice, thereby limiting the applicability of this technique.
- US-5,818,319 describes procedures for designing magnets, including superconducting magnets, shim magnets, and gradient magnets for magnetic resonance systems.
- the procedures involve the use of a simulated annealing procedure in which weighted spherical harmonics are included in the procedure's error function.
- the procedure has resulted in the development of previously unknown magnet designs.
- superconducting magnets have been designed that include at least one coil in which the current flow is opposite to that in adjoining coils.
- Such reversed flow in combination with a relatively large number of coils, e.g., more than 6 coils, have enabled the development of short, yet homogeneous, whole body magnets for use in magnetic resonance imaging (MRI).
- MRI magnetic resonance imaging
- magnet systems, and methods of designing the magnet systems still include some limitations.
- the use of simulated annealing processes is computationally expensive.
- the minimization function used in the simulated annealing process has multiple local minima, meaning that when a minima is found, there is no guarantee that this is the optimum, or the global solution. Consequently, using these techniques can result in non-optimal magnet designs.
- the present invention provides a method of determining a magnet arrangement for use in magnetic resonance imaging apparatus, the method including: a) determining a function representing current densities required within a magnet region to generate a field; b) determining a current density distribution required to generate a desired field, using the function; and, c) determining the magnet arrangement using the current density distribution, the magnet arrangement including a number of current carrying coils arranged within the magnet region.
- the method includes: a) dividing the magnet region into a number of elements; and, b) determining a current density for each element using the function to thereby determine the current density distribution.
- the method includes determining the current density distribution by optimizing the function.
- the function has a global minimum.
- the function is quadratic with respect to the current density within the magnet region.
- the function is based on the energy stored within the magnet region.
- (c) L is related to an inductance.
- the method includes defining the magnet region.
- the magnet region has an arbitrary shape positioned relative to at least one of: a) a bore; and, b) an imaging region.
- the magnet region substantially surrounds at least one of: a) a bore; and, b) an imaging region.
- the magnet region is rotationally symmetric with respect to a field axis.
- the field axis is aligned with a bore axis.
- Typically magnet region has a substantially cylindrical shape.
- the method includes, defining a desired field within at least one of: a) an imaging region; and, b) a stray field region.
- the method includes defining the imaging region to have a substantially predefined shape positioned with respect to the magnet region.
- the method includes defining an imaging region having a substantially spherical shape positioned on a field axis radially inwardly of the magnet region.
- the method includes defining a desired field including a substantially homogeneous magnetic field within an imaging region.
- the desired field has a homogeneity having a variation in the imaging region of less than at least one of: a) 100 ppm; b) 20 ppm; and, c) 10 ppm.
- the method includes defining a stray field region substantially surrounding the magnet region.
- the stray field region is positioned on the bore axis radially outwardly of the magnet region.
- the method includes defining a desired field including a field strength of less than a selected amount within the stray field region.
- the selected amount is less than, at least one of: a) 20 Gauss; b) 10 Gauss; and, c) 5 Gauss.
- a current density distribution has a series of extremities lying around a perimeter of the magnet region.
- the direction of current flow in the coils depends on the polarity of the extremities within the current density distribution.
- the method includes using the current density distribution to determine at least one of: a) coil locations within the magnet region; b) coil sizes; c) a current density within coils; d) a total current for coils; e) current flow directions within coils; and, f) coil winding directions.
- the method includes determining the coil arrangement based on extremities within the current density distribution.
- the coils are located on local positive maxima and local negative minima of the current density distribution.
- each current carrying coil is arranged substantially around a perimeter of the magnet region.
- each current carrying coil carries a current in an opposing direction to each adjacent coil.
- each current carrying coil carries a current in an opposing direction to each adjacent coil.
- the magnet region has a substantially cylindrical shape surrounding a field axis, each current carrying coil being arranged within the magnet region with a coil axis substantially aligned with the field axis.
- the method further includes optimising the coil arrangement.
- the method includes: a) defining a second function; and, b) optimising the second function to thereby optimise the coil arrangement.
- the method includes optimising the second function such that the coil arrangement has optimal coil current densities
- the second function has a global solution.
- the second function is quadratic with respect to the current density within the magnet region.
- the second function is a function of the energy stored within the coils.
- the method includes: a) defining coil constraints; and, b) optimising the second function using the coil constraints to thereby determine an optimised magnet arrangement.
- the coil constraints include at least one of: a) a minimum separation between coils to prevent coil overlap; and, b) an optimal current density flow for each coil.
- the optimal current density flow is smaller than a maximum current density.
- method includes selecting the maximum current density in accordance with a magnetic field strength and properties of superconducting material used in the current carrying coils.
- the method is performed at least in part using a processing system.
- the present invention provides a magnet arrangement for use in magnetic resonance imaging apparatus, the magnet arrangement including a number of current carrying coils arranged substantially around a perimeter of a magnet region, and wherein, for current carrying coils on a bore perimeter of the magnet region, each current carrying coil carries a current in an opposing direction to each adjacent coil on the bore perimeter.
- the current carrying coils are located substantially on extremities of a current density distribution determined for the magnet region.
- each coil carries a current in a direction defined by a polarity of the extremity.
- each coil carries a current in an opposing direction to each adjacent coil.
- each coil typically includes a number of current carrying windings.
- the number of current carrying windings is determined so that the coil generates a required magnetic field.
- the magnet region has an arbitrary shape positioned relative to at least one of: a) a bore; and, b) an imaging region.
- the magnet region is rotationally symmetric with respect to a field axis.
- the field axis is aligned with a bore axis.
- Typically magnet region has a substantially cylindrical shape.
- the magnet generates a desired field within at least one of: a) an imaging region; and, b) a stray field region.
- the imaging region has a substantially predefined shape positioned with respect to the magnet region.
- the imaging region has a substantially spherical shape positioned on a field axis radially inwardly of the magnet region.
- the imaging region has a substantially homogeneous magnetic field.
- the homogeneity has a variation of less than at least one of: a) 100 ppm; b) 20 ppm; and, c) 10 ppm.
- the stray field region substantially surrounds the magnet region.
- the stray field region is positioned on the field axis radially outwardly of the magnet region.
- the desired field has a field strength of less than a selected amount within the stray field region.
- the selected amount is less than, at least one of: a) 20 Gauss; b) 10 Gauss; and, c) 5 Gauss.
- Figure 1 is a flow chart of an example of a process for determining a magnet arrangement
- Figure 2A is a schematic side view of an example magnet arrangement generated using the process of Figure 1;
- Figure 2B is a schematic end view of the magnet arrangement of Figure 2 A;
- Figure 2C is a schematic side view of a second example magnet arrangement generated using the process of Figure 1;
- Figure 2D is a schematic side view of a third example magnet arrangement generated using the process of Figure 1;
- Figure 2E is a schematic perspective view of a fourth example magnet arrangement generated using the process of Figure 1;
- Figure 3 is a schematic diagram of an example processing system;
- Figures 4A and 4B are a flow chart of a second example of a process for determining a magnet arrangement
- Figure 5 is a schematic representation of a coordinate system used in determining a magnet arrangement
- Figure 6 is a schematic representation of regions used in determining a magnet arrangement
- Figure 7 is a schematic representation of the magnet geometries used in optimising a magnet arrangement
- Figures 8A and 8B are 3D and 2D representations of examples of minimum stored energy
- MSE current density profiles for 3 m long magnet domains for unshielded order 10 degree 0 configurations
- Figures 9A and 9B are 3D and 2D representations of examples of MSE current density profiles for 3m long magnet domains for shielded order 10 degree 2 configurations;
- Figures 1OA and 1OB are 3D and 2D representations of examples of MSE current density profiles for unshielded order 14 degree 0 2m length magnet configurations
- Figures HA and HB are 3D and 2D representations of examples of MSE current density profiles for unshielded order 14 degree 0 ⁇ m length magnet configurations
- Figures 12A and 12B are 3D and 2D representations of examples of MSE current density profiles for shielded order 16 degree 4 2m length magnet configurations;
- Figures 13A and 13B are 3D and 2D representations of examples of MSE current density profiles for shielded order 16 degree 4 Im length magnet configurations;
- Figures 14A and 14B are 3D and 2D representations of examples of MSE current density profiles for unshielded order 16 degree 0 ⁇ m length magnet configurations;
- Figures 15A and 15B are representation of the resulting DSV magnetic field with final coil arrangement and stray fields for the initial magnet configuration of Figure 14B;
- Figures 16A and 16B are 3D and 2D representations of examples of MSE current density profiles for shielded order 14 degree 4 1m length magnet configurations;
- Figures 17A and 17B are representations of the resulting DSV magnetic field with final coil arrangement and stray fields for the initial magnet configuration of Figure 16B;
- Figures 18A and 18B are representations of the resulting DSV magnetic field with final coil arrangement and stray fields for a short bore clinical magnet
- Figures 19A and 19B are representations of the resulting DSV magnetic field with final coil arrangement and stray fields for a short bore 3.0T clinical magnet;
- Figures 2OA and 2OB are representations of the resulting DSV magnetic field with final coil arrangement and stray fields for a high field clinical magnet; and, Figures 21 A and 21B are representations of the resulting DSV magnetic field with final coil arrangement and stray fields for an open bore clinical magnet.
- a function is determined representing the current densities required within a magnet region in order to generate a given field.
- the function is based on the stored energy within the magnet coils, and hence can be quadratic with respect to the current density, when combined with a term representing a coil inductance.
- the use of a function that is quadratic with respect to the current density means that the function has a single global solution for a given desired field.
- a current density distribution required in order to generate a desired field is determined using the function.
- the desired field may be any suitable field required for performing MRI, and will typically therefore require the presence of a suitably homogenous field in an imaging region, and a low external stray field magnitude.
- the desired field will therefore depend on factors such as the nature of the MRI process being performed.
- the current density is typically determined in any one of a number of ways depending on the nature of the function used, but in one example, this involves finding a minimum or maximum of the function for the desired field, as will be described in more detail below.
- the resulting current density distribution has a series of extremities lying around the perimeter of the magnet region.
- the current density may have a relatively large number of maxima and minima of a common polarity, so that for example, positive maxima are adjacent to positive minima, or vice versa.
- the number of such extremities becomes smaller, with a further reduction in size resulting in the adjacent extremities having opposite polarities, such that positive maxima are located adjacent to negative minima.
- this can be used to determine the magnet arrangement at step 120.
- the magnet arrangement will typically specify one or more magnet parameters, such as a number and location of current carrying coils within the magnet region, the respective current density and/or total current required for each coil, the direction of current flow within the coils, or the like.
- the arrangement is at least partially based on the location and/or magnitude of extremities, such as local positive maxima and local negative minima, in the ideal current density distribution obtained for the specified magnet parameters.
- the magnet arrangement determined in step 120 can be optimised further, using an optimisation strategy. This can be performed in any suitable manner, and may be used to refine the magnet arrangement, for example to ensure that the current density for each current carrying coil is feasible, and to ensure the peak field on the coil is within acceptable ranges.
- a cylindrical magnet region 200 is provided surrounding a cylindrical bore 220, defining a bore axis 225.
- the magnet region 200 contains a number of current carrying coils 201, having their axes aligned with the bore axis 225, which are used to generate a desired magnetic field within an imaging region 230.
- This configuration results in a magnetic field that is rotationally symmetric about a magnetic field axis (not shown) that is aligned with the bore axis 225.
- a coil region 210 is also typically provided between the magnet region 200 and the bore 220 for containing RF coils, shim coils and/or gradient coils, as required for the respective MRI process.
- the coils 201 are generally spaced apart around the perimeter of a magnet region 200, which results from performing the methodology described above. Furthermore, the number, size and shape of the coils is not intended to be limiting and is merely for illustrative purposes, as will become apparent from the specific examples described in more detail below.
- each of the coils The direction of current flow in each of the coils is indicated by the "+” and "-" symbols, showing that in at least some of the resulting magnet arrangements, the current flow in each adjacent coil is in an opposite direction to that in each other adjacent coil. This is not essential, and arrangements with current flows in adjacent coils in the same direction are described. However, in general the opposing current flow arrangement results in a more optimal and compact design.
- current flow in at least the coils along a bore perimeter boundary 202 adjacent the bore 220 are typically in opposing directions.
- current flow in each coil is opposite the current flow in each adjacent coil for the entire perimeter.
- Current flow in opposing directions may be achieved in any one of a number of ways, such as by reverse winding adjacent coils, or by controlling the current flow in each coil.
- the magnet arrangement described above and in particular, the positioning of coils around the perimeter of the magnet region, and the reverse current directions for adjacent coils results in a significantly improved field generating capability.
- this can generally be produced by a magnet arrangement having a shorter axial length than can be achieved using prior art techniques and arrangements.
- the arrangement typically results in improved homogeneity within the imaging region, and a reduction in stray field (or fringe field) levels outside the magnet region.
- magnet region 240 is still rotationally symmetrical about the bore axis 225, but has a non-rectangular cross section, resulting in a non-circular imaging region 245. It is apparent from this, that a magnet region having any desired cross sectional shape can be used.
- magnet region 250 is rotationally symmetrical about a field axis 251, which is substantially perpendicular to the bore axis 225. It is apparent from this, that the field axis .251 need not be coincident with the bore axis 225.
- two magnet regions 260 are provided, situated on either side of an effective bore axis 225.
- the magnet region 260 is not rotationally symmetrical, but does define a field axis that is coincident with the effective bore axis 225.
- the magnet region has any arbitrary shape that is optionally rotationally symmetric with respect to a bore or field axis. However, this is not necessary and for example, non rotationally symmetric arrangement can be used.
- the magnet region surrounds the imaging region in the above examples, the imaging region can instead be offset from the magnet regions, as occurs for example in open magnet configurations.
- the above described process is performed at least in part utilising a processing system, an example of which will now be described with reference to Figure 3.
- the processing system 300 includes a processor 310, a memory 311, an input/output device, such as a keyboard and mouse 312, and an optional external interface 313 coupled together via a bus 314.
- the optional external interface may be coupled to a database 315, allowing the processing system 300 to store data and/or access previously stored data.
- the processor 310 typically executes applications software stored in the memory 311, to allow the processor 310 to perform required calculations and/or display results. This can include, for example, performing analysis of the function and desired field in order to generate the current density distribution, displaying the current density distribution to a user, determining the magnet arrangement and performing further optimisation. It will be appreciated that these processes can be performed automatically, but typically involve at least some input or other control by the user.
- processing system 300 may be a suitably programmed computer system, such as a laptop, desktop, PDA, computer server, or the like, although alternatively the processing system 300 may be formed from specialised hardware.
- a magnet region, stray field region and imaging region are defined.
- the regions will typically be defined based on a combination of the MRI imaging requirements and the required physical size of the resulting arrangement.
- the imaging region is typically defined based on the need to encompass a certain physical volume depending on required imaging purposes. It will be appreciated that a number of different standard configurations are known, such as short bore configuration or the like, and these can therefore be generated by appropriate configuration of the regions.
- Defining the regions will typically be achieved by allowing the user to input parameters into the processing system 300 representing the respective regions. This may be achieved in any suitable manner and can include the use of a graphical user interface for displaying a representation of the defined field regions, or the like.
- a cost function is defined based on the current density within the magnet region.
- the cost function is typically proportional to the energy stored within the magnet region, which in turn depends on the current density and an inductance within the region. This leads to an equation of the form:
- / is the current density within the magnet region
- L is related to an inductance
- the inductance and current density are typically summed over finite elements defined throughout the magnet region, as will be described in more detail below. Accordingly, in this instance, the inductance corresponds to the inductance that a coil within the region may have and can include a self inductance and/or a mutual inductance.
- the cost function By basing the cost function on the square of the current density, the function has a single global maximum or minimum (depending on whether the function is negative or positive), thereby leading to a single optimum configuration for a desired field. Furthermore, as the cost function is indicative of the energy stored in current carrying coils located within the magnet region, finding the minimum therefore minimises the total stored energy, which in turn minimises quenching strains and the amount of superconducting wire used in the design.
- the cost function can be defined in a case-by-case basis, but in one example is pre-defined in applications software executed by the processing system 300.
- a desired field configuration is determined.
- the desired field is determined based on imaging field and stray field requirements, which will typically require that the magnetic field is substantially homogenous across the entire volume of the imaging region, and typically has homogeneity of at least 100 ppm, typically better than 20 ppm, and preferably better than 10 ppm.
- the stray field typically needs to be minimised to avoid undue interference with equipment external to the magnet configuration, and therefore preferably has a strength below 20 Gauss, and preferably below 15, 10 or even 5 Gauss.
- the field requirements can be defined manually by having a user input appropriate parameters. Additionally, and/or alternatively, appropriate parameters may be pre-defined in the applications software executed by the processing system 300.
- the cost function is optimised for the desired field based on the definitions provided in step 410.
- the manner in which the cost function is optimised will vary depending on the preferred implementation. However, as mentioned above, by using the above described form of cost function, this leads to a single global minima for a given desired field, which in turn allows a single solution to be derived. Accordingly, this allows the processing system 300 to perform appropriate calculations, allowing the minima to be determined.
- the processing system 300 generates a current density map which can then be optionally displayed to a user via the I/O device 312, using a suitable user interface.
- the current density map represents the current densities required within the magnet region in order to generate the desired field, and particular example current density maps will be described in more detail below.
- coil parameters are determined based on the current density distribution. This may be achieved in any one of a number of ways such as by manual definition by a user, or through automatic definition in the processing system 300. Thus, for example, the user can be presented with a representation of the current density map, allowing the user to indicate preferred coil parameters using the I/O device 312, such as a mouse.
- the parameters determined can include any one or more of coil locations, coil sizes, coil shapes, current directions, coil winding directions, or the like.
- Coil locations are typically defined to correspond to the locations of extremities in the current density distribution, whilst coil sizes and shapes depend on magnitude of the extremities.
- the coil winding direction then depends on whether the current density for a given maxima or minima is positive or negative. As discussed above, the coil winding direction may represent a physical direction for the coil winding or alternatively may represent a direction of current flow through the coil, depending on the preferred implementation.
- the coil arrangement represents an unoptimised coil layout. Accordingly, in one example, further optimisation may be performed.
- a second cost function is determined. This is typically of a similar form to the cost function described above, and a specific example will be described in more detail below.
- the cost function can be pre-defined in the applications software executed by the processing system 300.
- coil constraints are defined.
- the coil constraints will typically include limitations such as providing at least a minimum separation between coils to prevent coil overlap, as well as providing a maximum current density flow for each coil. These represent physical constraints on coils which are practically implementable, and are typically selected based on a required magnetic field strength and properties of superconducting material used in the current carrying coils.
- the coil layout cost function can be optimised to allow an optimised coil configuration to be determined.
- the optimisation is typically performed using quadratic sub- problems given constraints, as will be described in more detail below, although any suitable technique may be used. It will be appreciated that in this instance, instead of optimising for current density throughout the magnet region, the optimisation is performed specifically with respect to the coils and their current densities, thereby differing from the previous optimisation problem.
- the obtained coil parameters for each coil are then compared to allowable criteria to ensure that the coil location and peak field constraints are met.
- this can include ensuring the coils do not overlap, and that the maximum peak field on the coil is within an acceptable range.
- the optimisation can be repeated with different coil constraints, if this is required at step 450. Otherwise, the resulting coil arrangement can be provided as an output by the processing system 300 at step 455.
- the magnetic field produced by an arbitrarily shaped electric current carrying conductor is expressed as the sum of an infinite series of spherical harmonics.
- the amplitude and sign of each spherical harmonic expansion term depends on the coil geometry, current strength, winding direction and relative positions of coils in a particular magnet configuration.
- a collective set of coils can be organised in space to meet the needs of a specific application by appropriate choice of size, current magnitude and direction, and spacing, to emphasise certain spherical harmonic expansion terms that define the magnetic field produced by the current carrying coils themselves.
- FIG. 5 An example of the geometry and reference frame for a cylindrical coil in space is shown in Figure 5, which defines the magnetic field at point P(r, ⁇ ) produced by a superconducting coil, having cross section 500 located in the illustrated yz-plane.
- Figure 5 An example of the geometry and reference frame for a cylindrical coil in space is shown in Figure 5, which defines the magnetic field at point P(r, ⁇ ) produced by a superconducting coil, having cross section 500 located in the illustrated yz-plane.
- appropriate symmetry is assumed to characterize the cylindrical nature of the problem, and the problem is simplified to 2D due to the inherent symmetry.
- the axial component of the magnetic field at a point (r ⁇ r Q , ⁇ ) in an axisymmetric configuration comprising current carrying circular filaments coaxial with the z-axis is given by: where ⁇ 0 is the permeability of free space; / is the filament current;
- PTM (cos ⁇ ) is the associated Legendre polynomial evaluated at the appropriate location in space.
- coordinates ( ⁇ 1 , Z 1 ) and (y 2 ,z 2 ) define a rectangular conductor cross-section in the ⁇ z-plane as shown in Figure 5.
- the harmonic coefficients a n and ⁇ n can be computed analytically or numerically.
- the analytic expressions for the coefficients are obtained by solving the given integral for a n and ⁇ n , although alternatively Gaussian quadrature can be used to obtain the individual values of a n and ⁇ n , and typically this procedure is both accurate and efficient, when compared to the analytic expressions.
- the first two harmonic coefficients for the inner region given in analytical form are:
- the process is performed in two primary stages.
- This first stage is to determine an initial layout of the superconducting coils and the associated current densities in a predefined domain subject to constraints, such as the homogeneity of the DSV and the size of the magnet stray field. This is achieved by changing the size of the magnet domain and by adjusting the number of internal and external harmonic coefficients to be vanished.
- the second stage is the refinement of coil geometries to enhance the field homogeneity, to decrease the stray field (or fringe field) of the magnet and to restrict peak field values at the coils to an acceptable range.
- the regions are typically configured as shown in Figure 6.
- the magnet region 600 lies within a region 610 centred at an origin 620.
- the region 610 has substantially spherical shell shape.
- this is not essential, and any desired shape of region and magnet region can be employed using this method.
- the stray field region 630 is positioned externally to an outer boundary 611 of region 610, while the imaging region 640 is positioned internally within an inner boundary 612 of region 610.
- the domain of interest is divided into K small elements 601, as shown in the upper representation of the magnet region 600 in Figure 6.
- the current densities I k associated with individual elements are then determined by minimizing the cost function F mt , which is formulated as a stored energy sum: subject to: K-I
- Bo is the desired magnetic field strength at the iso-centre; a.k, n and ⁇ icm are the spherical harmonic terms of element k;
- M specifies the number of external harmonic coefficients
- N specifies the number of internal harmonic coefficients, given that K ⁇ M+N;
- L k is the inductance of element & with its dimensions shown in Figure 6; and A k is the cross-sectional area of a single wire element.
- M and JV help define the size of the stray field and the DSV, respectively.
- M and N are increased to reduce the size of the stray field and to increase the size of the DSV. If a magnet design has N-I internal coefficients and M external coefficients vanished, it is referred to as an N order M degree magnet design.
- iC is the number of elements in one quarter of the magnet domain.
- the cost function defined in equation (4) is formulated to ensure that the stored energy within the coils is minimized, and consequently magnet training and quenching strains will be kept to a minimum.
- the formulated cost function also provides the benefit of minimizing the amount of superconducting wire used in the design, since the coil inductance is proportional to the conductor volume when restrictions on the length of the magnet domain are enforced.
- the cost function F m is solved using the general quadratic program (QP)
- This stage of the magnet design process enables the generation of unique current density maps, named the minimum stored energy (MSE) current density map, in which the coils are embedded.
- MSE minimum stored energy
- a current density map is obtained that has several local maxima and minima within the magnet domain referred to as extremities.
- the number of extremities is proportional to the number eliminated spherical harmonics, and notably these extreme points are distributed along the boundary or perimeter of the magnet domain.
- the next step is to establish and refine the superconducting coil geometries to enhance the magnetic field homogeneity in the inner field, as well as, to satisfy other constraint requirements, including the peak magnetic field condition on the superconducting coils and the stray magnetic field strength.
- Superconducting coils are placed in the magnet domain, based on the positioning of extremities in the form of local positive maxima and local negative minima.
- the coils are initially overlapped on the extreme point locations with their initial cross sectional areas being proportional to the value of the overlapping current densities. This process of identifying and locating coils will be described in more detail below.
- the constant current coil geometries are refined by using a non-linear optimization method that minimizes the cost function F refine defined similarly as F mi :
- K is the number of the superconducting coils in the magnet domain.
- Constraint (9) in this case therefore becomes:
- Z is the number of the superconducting coils in one quarter of the magnet domain.
- the current densities are positive and are the same for all elements, and hence for the coils.
- the optimization process can also be used when different current densities on different coils are needed.
- the sign of the current in a particular coil is implied by the order of the y ⁇ and y 2 coordinates, as shown in Figure 5. lfy x > y 2 , then the current has a positive sign, otherwise it has a negative sign. The need for negative currents within the computations is eliminated by using such an approach.
- F re ⁇ m is a constrained non-linear optimization problem that requires the use of an appropriate non-linear optimization algorithm to obtain the coil layout.
- SQL sequential quadratic programming
- coil overlap is avoided by dividing the magnet domain into several layers and extra geometrical constraints based on the current density map are introduced to limit the movement of the coils. This step is fundamentally correct, since the current density maps do not suggest that the coils should be overlapped. In particular, limits on the ⁇ -coordinate of the individual coils are imposed by breaking the domain into layers, and large axial movements are restricted by imposing z-coordinate bounds.
- each of the layers has respective boundaries provided at distances Yo, Yi, Y 2 , Y 3 from the origin.
- the coils are generally designated b ⁇ , where / is a layer identifier, and p is a coil number.
- the separation between the coils within each layer are generally designated ⁇ / , p associated with coil p for a particular layer /.
- the values for a, and b l must be non-negative, and in any given layer the sum of them must not be larger than the half length of the domain.
- the extreme current densities are distributed over the domain boundary, hence, the upper and lower layers can have multiple coils and any layers between them consist of a single coil.
- the magnetic field at the superconducting coils is calculated using available methods, such as outlined in Forbes, L.K., S. Crozier, and D.M. Doddrell, Rapid Computation of Static Fields Produced by Thick Circular Solenoids. IEEE Transactions on Magnetics, 1997. 33(5): p. 4405-4410.
- the magnetic fields are then tested for peak field criteria. If within the coils the peak field is greater than the allowable limit, then the individual layers are adjusted, such that the spacing between the coils is increased. For example as shown in Figure 7, for the depicted three layer configuration, Y 1 and Y 2 are changed such that
- the optimization process is then repeated to obtain the new coil layouts according to the new layer constraints. It may happen that this process of iterative refinement needs to be repeated two or three times to ensure that the best coil layout can be obtained, for a given maximum level of peak magnetic field for the coils.
- Both unshielded and shielded magnets are designed using the outlined strategy to generate the inner field, and also, to gauge the stray field produced by the magnets. The results are also used to illustrate the location of the MSE current density map extremities and alterations to these extremities as the size of the magnet domain is varied.
- Figures 8 A and 8B show 3D and 2D MSE current density profiles with contours for 3m long magnet domains for unshielded order 10 degree 0 configurations, whilst equivalent shielded order 10 and degree 2 configurations are shown in Figures 9 A and 9B.
- Figures 1OA and 1OB show 3D and 2D MSE current density profiles with contours for unshielded order 14 degree 0 2m length magnet domains, with ⁇ m length domains being shown in Figures 1 IA and 1 IB.
- Figures 12A and 12B show 3D and 2D MSE current density profiles with contours for shielded order 16 degree 4 2m length magnet domains, with Im length domains being shown in Figures 13A and 13B.
- Figure 13 provides the current density map for the shortened design.
- the predicted coil layout due to the extreme current density values indicates alternating currents within the individual magnet coils.
- the current density map allocates the coils on the perimeter of the domain.
- Short Bore Unshielded Magnet Design In the following cases, the domain is limited in length to Xm with bore diameter of Im, hence qualifying the designs as short MRI magnets.
- the superconducting wires used in the designs are taken from Sciver, S. W. V. and K.R.son, Superconducting Magnets Above 20 Tesla. Physics Today, 2002(August): p. 37-42. All of the coils are formed using ⁇ mm x ⁇ mm NbTi wires, by limiting the current to a level below 180 ⁇ 4 and the peak magnetic field on the superconducting coils to be less than 9T .
- Figures 14A and 14B are 3D and 2D MSE current density profiles with contours for order 16 degree 0 magnet arrangements.
- the resulting coil layout defined by the current density profile is shown in Figure 14B.
- the allocation of the individual coils aligns with the current density map peaks, and the size of the coils is proportional to the magnitude of the current density at that location.
- the initialised coils are reflective of the results obtained through the first initial layout stage.
- the second optional optimisation stage is then seeded using the coil allocation of shown in Figure 14B, and rapid convergence is achieved, due to the fact that the initial seed is highly accurate. Once the optimization of stage two has converged, by changing the location and size of the blocks, the resultant magnetic field is calculated.
- FIG. 15A An example of the final optimised magnet configuration and the resulting magnetic field is shown for the DSV in Figure 15A and for the stray fields in Figure 15B.
- the innermost contour corresponds to lppm , followed by the IQppm contour, and the stray field with 5, 10, 15 and 20 gauss contour lines.
- the DSV is 50cm in diameter at the lppm contour line, and approximately 56cm in diameter to the 10 ppm contour line.
- the footprint of this unshielded magnet is quite large, as can be seen in Figure 15B.
- the final configuration for the unshielded case has an alternating current direction coil layout around the perimeter of the magnet domain. It should also be noted that the largest coil is actually not on the inner layer of the magnet (i.e. near the bore perimeter 202), but rather on an outer perimeter of the magnet region 200.
- the external magnetic field harmonic coefficients are used to reduce the stray field, which means that the number of coils has to be increased to allow for appropriate magnetic field definition.
- Table 2 provides the dimensions and locations of the final coil layout, after optimisation.
- the current in the NbTi wire is below the current carrying capability of the wire, and the peak field was calculated to be 8.98867 1 , which is also below the peak magnetic field requirement.
- FIGS 17A and 17B The DSV and stray magnetic fields for the final coil layouts following optimisation are shown in Figures 17A and 17B respectively.
- the innermost contour corresponds to ⁇ ppm, followed by the lOppm contour, whilst the stray field in Figure 17B shows 5, 10, 15 and 20 gauss contour lines.
- the DSV has a 40cm diameter to the lppm contour line and a diameter of 50cm to the ⁇ 0ppm contour line.
- An important observation in this design is that the most outer coils do not necessarily have to be opposing current coils to reduce the stray field of the magnet, but rather, these coils are used in conjunction with the rest of the coils to obtain an overall effect satisfying both DSV and stray field requirements.
- the stray field at the 5 gauss level extends no more than Am from the centre of the magnet.
- Figures 18A and 18B show DSV fields with contours at 0.25, 1 and 10 ppm lines, and stray fields with contours at 5, 10, 15 and 25 gauss for a short bore clinical magnet.
- the properties of the resulting configuration are as follows: Bore diameter: Im Bore length: 1.28m
- Figures 19A and 19B show DSV fields with contours at 0.25, 1 and 10 ppm, and stray fields with contours at 5, 10, 15 and 25 gauss for a short bore 3.0T clinical magnet.
- the properties of the resulting configuration are as follows: Bore diameter: Im
- Figures 2OA and 2OB show DSV fields with contours at 0.25, 1 and 10 ppm, and stray fields with contours at 5, 10, 15 and 25 gauss for a high field clinical magnet.
- the properties of the resulting configuration are as follows: Bore diameter: Im Bore length: 1.8m
- Figures 21 A and 21B show DSV fields with contours at 0.25, 1 and 10 ppm, and stray fields with contours at 5, 10, 15 and 25 gauss for an open bore clinical magnet.
- the properties of the resulting configuration are as follows: Gap: 60cm Pole length: 0.4m Total length: 1.44m
- the above described processes provide a method of designing magnet arrangements, and in particular for designing superconducting magnet arrangements suitable for use in MRI imaging apparatus.
- the processes have the ability to arrange coils in a manner that ensures that the overall dimensions and stored magnetic energy are minimized with peak current and peak magnetic field in acceptable ranges.
- the process uses a magnet region or domain that is treated as current density maps, in which, superconducting coils are embedded.
- the current density maps from which the coils themselves are derived are unique, and allow a minimum stored energy configuration to be derived.
- a second optimisation phase may also then be performed to generate final coil layouts that take into account coil dimensions for required field linearity, and peak and stray field minimization.
- the stray field of the shielded magnet designs are very small whilst maintaining a large DSV, when compared to the overall magnet dimensions.
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AU2008902243A AU2008902243A0 (en) | 2008-05-08 | Magnet arrangement | |
PCT/AU2009/000572 WO2009135264A1 (en) | 2008-05-08 | 2009-05-07 | Arrangement of coils for mri apparatus |
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JP3705861B2 (ja) * | 1996-03-21 | 2005-10-12 | 株式会社日立メディコ | 超電導磁石装置及びその着磁調整方法 |
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